For $x<0, \frac{d}{d x}\left[|x|^x\right]=$

If $y=x-x^2$, then the rate of change of $y^2$ with respect to $x^2$ at $x=2$ is

If $T=2 \pi \sqrt{\frac{L}{g}}, \mathrm{~g}$ is a constant and the relative error in $T$ is $k$ times to the percentage error in $l$, then $\frac{1}{K}=$

The angle between the curves $y^2=2 x$ and $x^2+y^2=8$ is